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On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb (1999)

Annales de l'institut Fourier

Let M = G / H be a real symmetric space and 𝔤 = 𝔥 + 𝔮 the corresponding decomposition of the Lie algebra. To each open H -invariant domain D 𝔮 ⊆ i 𝔮 consisting of real ad-diagonalizable elements, we associate a complex manifold Ξ ( D 𝔮 ) which is a curved analog of a tube domain with base D 𝔮 , and we have a natural action of G by holomorphic mappings. We show that Ξ ( D 𝔮 ) is a Stein manifold if and only if D 𝔮 is convex, that the envelope of holomorphy is schlicht and that G -invariant plurisubharmonic functions correspond to convex H -invariant...

On the removable singularities for meromorphic mappings.

Evgeny M. Chirka (1996)

Publicacions Matemàtiques

If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.

On the spectrum of A(Ω) and H ∞ ( Ω )

Urban Cegrell (1993)

Annales Polonici Mathematici

We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.

Relative tangent cone of analytic curves

Danuta Ciesielska (1999)

Annales Polonici Mathematici

The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in ℂ m with an isolated intersection.

Some envelopes of holomorphy

Edgar Lee Stout (2009)

Annales Polonici Mathematici

We construct some envelopes of holomorphy that are not equivalent to domains in ℂⁿ.

Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif

Michel Lassalle (1978)

Annales de l'institut Fourier

Soit H un groupe analytique compact : son complexifié universel G est un groupe analytique complexe réductif. On introduit dans G une classe de “domaines de Reinhardt généralisés”, bi-invariants par H et caractérisés par une “base”, définie dans une sous-algèbre abélienne maximale de l’algèbre de Lie du groupe H et invariante par le groupe de Weyl.On donne une caractérisation par leurs coefficients de Fourier-Laurent des fonctions holomorphes dans un tel domaine. On montre que l’enveloppe d’holomorphie...

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